There are significant efforts to develop continuum theories based on atomistic models. These atomistic-based continuum theories are limited to zero temperature (T=0K). We have developed a finite-temperature continuum theory based on interatomic potentials. The effect of finite temperature is accounted for via the local harmonic approximation, which relates the entropy to the vibration frequencies of the system, and the latter are determined from the interatomic potential. The focus of this theory is to establish the continuum constitutive model in terms of the interatomic potential and temperature. We have studied the temperature dependence of specific heat and coefficient of thermal expansion of graphene and diamond, and have found good agreements with the experimental data without any parameter fitting. We have also studied the temperature dependence of Young’s modulus and bifurcation strain of single-wall carbon nanotubes.

Temperature dependence of Young’s modulus for graphene predicted by the present continuum theory based on interatomic potentials. Here the Young’s modulus is normalized by its counterpart at zero temperature. The molecular dynamics simulation results for a (10,10) carbon nanotube (38) based on a different interatomic potential (39) are also shown.

Temperature dependence of the coefficient of thermal expansion α for graphene predicted by the present continuum theory based on interatomic potentials. The experimental data of graphite (36) are also shown.

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